1. Field of the Invention
The present invention relates to a recording medium storing an original data generation program, an original data generation method, an original fabricating method, an exposure method, and a device manufacturing method.
2. Description of the Related Art
Recently, higher resolution has been demanded in a projection exposure apparatus for projecting a circuit pattern drawn on an original plate (hereinafter, referred to as an original, such as a mask or a reticle) onto a wafer through a projection optical system. As methods for achieving high resolution, a method using a projection optical system with a high numerical aperture (NA), a method for using a shorter exposure wavelength (λ), and a method for reducing a k1 factor are known.
As the k1 factor becomes smaller, a mask pattern deviates from a pattern formed on a wafer. In the related art, an optimum mask pattern is calculated by repeatedly modifying the mask pattern until an intended pattern (target pattern) is formed on a wafer.
However, recently, a method for determining a mask pattern from an intended pattern to be formed on a wafer plane has attracted the attention. This method relates to the so-called inverse lithography. The idea of the inverse lithography was suggested in the 1980s. However, a calculation method was not established at that time and a practical mask designing method was not realized with the capacity of computers used in those days.
Thanks to recent establishment of a calculation method and recent improvement in the capacity of computers, various inverse lithography techniques have been proposed. Methods disclosed in US Patent Application Publication No. 2006/0269875 and U.S. Pat. No. 7,124,394 are available. Additionally, a method described in “Solving inverse problems of optical microlithography”, Proc. of SPIE, USA, SPIE press, 2005, Vol. 5754, pp. 506-526 (written by Yuri Granik) is considered as a standard method of the inverse lithography.
In the above-described related art, a light intensity distribution on a wafer is represented as a sum of a plurality of eigenfunctions. The complex calculations used can require a lot of time. Moreover, solution of an optimization problem in the related art generally takes a lot of time. The related art thus can be both complex to implement and slow.